In a common description, a stochastic process with the Markov property, or memorylessness, is one for which conditional on the present state of the system, its future and past are independent[1].
Often, the term Markov chain is used to mean a Markov process which has a discrete (finite or countable) state-space. Usually a Markov chain would be defined for a discrete set of times (i.e. a discrete-time Markov Chain)[2] although some authors use the same terminology where "time" can take continuous values.[3] Also see continuous-time Markov process.
Craigslist killer Philip Markoff and victim Julissa Brissman led secret lives
Sunday, April 26th 2009, 1:05 AM
Garfinkel/Pool Accused 'craigslist killer' Philip Markoff stands during his arraignment in Boston Municipal Court.
Mark Pines Markoff is charged with the murder of Julissa Brisman.
Their lives intersected in the anonymous fog of the Internet, tailor-made for a young woman who made a living meeting strangers in hotels and a man looking for easy victims.
Julissa Brisman was from the upper West Side, a beautiful aspiring actress whose tough life drove her to drink and to a shadowy job offering massages on craigslist.
Philip Markoff is clean-cut, studying to be a doctor, and planning a dream wedding with his college sweetheart. Police say he also had a secret life, robbing and brutalizing women he met on craigslist.
Their shadow worlds came to light when she was shot dead in a posh Boston hotel and he was arrested as the "Craigslist Killer."
All who knew them were shocked, but looking back, there clearly were some signposts along their disparate journeys to that fateful moment 12 nights ago in Boston.
***
Brisman, who would have turned 26 on Friday, lived on W. 107th St., just outside Central Park, and had a younger sister she doted on.
She was 5-feet-5, had shimmering blond hair. A photo of her on a Web site about cell phone safety shows her with pale pink pouting lips, her almost-golden eyes giving a sultry look.
"Vivacious," "fun," "hardworking," they all said of her.
Markoff, 23, is a tall, blond, Abercrombie & Fitch type. He was raised in an upstate town, Sherill, near Syracuse. His father is a dentist and his mother worked in a casino shop. He has an older brother, Jon.
Markoff excelled in Vernon-Verona-Sherrill High School, where he was on the bowling and golf teams, and was an honors student who liked poker.
"Polite," "clean-cut," "kind," "funny," they all said about him.
When Markoff was shining in high school, Brisman was 19, a sales associate in Macy's Herald Square. She was arrested in June 2002 for stealing $3,700 in merchandise from Macy's. Cops say she falsely credited her store account for returned items and used the bogus credits to buy other things. Brisman apparently did not serve any time for this.
Markoff graduated from high school in 2004 and went to SUNY Albany to study biology. In 2005, he revealed juvenile subterfuge, and a disturbing roughness to fellow student Morgan Houston.
Houston said that before their cram sessions, Markoff would study for hours. He was a better student than she, but pretended he didn't know the material so he could spend time with her.
He frightened her once by grabbing her, shoving her against a wall on campus and trying to kiss her as they walked on campus late at night.
"I couldn't physically get him off of me," Houston told the Daily News. "Thankfully, he wasn't on top of me." A male student passing by pulled him off her.
In 2006, Brisman's life took another downward detour. She was arrested and spent six days in Rikers Island. The case is sealed and no information is available on why she was jailed.
Everything was falling into place for Markoff. He met his fiancée, Megan McAllister, when they worked at the Albany Medical Center emergency room. He graduated from SUNY in 2007 and entered Boston University School of Medicine.
That year, Brisman found some fame by making a public service ad for the Near Ear Foundation on the dangers of distraction when talking on a cell phone while walking down the street.
Last May, Markoff and McAllister got engaged. He proposed on a horse-drawn carriage ride in Connecticut. They enjoyed gambling at Foxwoods Resort.
They posted a bridal registry online, listing Vera Wang wine goblets, sterling silver picture frames and Emerilware pots and pans. On the Knot Web site they announced they'd marry on a Jersey Shore beach on Aug. 14.
A lab partner who worked closely with Markoff at Boston University would later tell reporters she was troubled by his profound mood swings.
Brisman battled alcohol abuse, and then enrolled in a two-year City College program to become a drug and alcohol counselor.
In January, a friend said, she did a photo shoot in a pink bikini for a tanning salon ad. She also worked on music videos.
Another friend said she had been paid $1,000 to fly to private parties in Chicago and strut in a bikini or topless; eye candy, nothing more. Brisman used some of the money to buy her teenage sister a computer.
***
Three weeks ago, a cousin of Brisman says, the aspiring actress told her mother, Carmen Guzman, she was going to Boston to meet a medical student she had met on the Internet.
"My aunt was like 'You better be careful, because people who are on the Internet are sometimes bad people,'" the cousin told a reporter.
On April 10, a 29-year-old Las Vegas woman, Trisha Leffler, who also advertised as a masseuse on craigslist, was attacked at the Boston Westin Copley hotel. She later identified Markoff as the man who bound her with plastic ties and robbed her.
Two days later, on April 12, Markoff was gambling at Foxwoods. Two days after that, he returned to Boston, to meet Brisman in a 20th-floor room at the posh Marriott Copley Place, arranged by e-mails, cops say.
He allegedly bludgeoned her and shot her three times and left her in a pool of blood.
The next day a friend of Brisman's looked at Brisman's e-mail account and saw messages from a man Brisman was scheduled to see the night before for a massage. The friend immediately forwarded the e-mail to detectives.
On April 16, it was another night of gambling at Foxwoods, with Markoff winning $5,300.
That same night, he is suspected of an attempted robbery in the Warwick, R.I., Holiday Inn Express of a woman who had posted a craigslist ad as a stripper. She was held at gunpoint before her husband entered the hotel room and her attacker fled.
Last Saturday, Boston cops pinpointed the physical location of the computer used to send the e-mail to Brisman - the luxury towers in Quincy, Mass., where Markoff lives with his betrothed.
On Monday, cops staked out his building, and saw Markoff and McAllister leave. They were headed to Foxwoods. Cops pulled them over on I-95 and arrested him.
***
Brisman's friends said they didn't know she had a secret life.
"What we know is that Miss Brisman was advertising masseuse services on craigslist," said Boston police spokeswoman Elaine Driscoll.
McCallister insisted her fiancée could not hurt a fly.
On Tuesday, Markoff pleaded not guilty to Brisman's murder. Evidence mounted: cops found a gun, duct tape, and plastic restaints in his apartment, along with panties reportedly from the victims stuffed in a copy of a "Gray's Anatomy" textbook.
Some speculate the motive for the attacks was to finance his gambling habit, but Vernon Geberth, a former NYPD homicide investigator and expert on sexual murders, doesn't buy the gambling theory. "He's a sexual predator, no matter what they say."
***
They are linked in the virtual world forever, their lives laid bare to millions.
Last Wednesday, a new Facebook group called "Phil Markoff is Innocent Until Proven Guilty" was launched, to rally against the media "that has forgotten that people like Phil are suspects, not killers."
Markoff is shown in a red high school graduation gown, holding a red mortarboard, with a neat haircut, tinted eyeglasses, posed against a puffy cloud-dotted sky.
The Near Ear Fundation's Web site featured a memorial page with an almost inappropriately sexy photo of Brisman. Her hair is tousled, her doe eyes peer over her bare shoulder. A videographer she worked for wrote a poem about killers.
Markoff's and McAllister's Knot Web page noted, "114 days to go!"
That same day, in the real world, Markoff sat behind bars in a Boston jail - and Brisman's mother cried in the Ortiz Funeral Home in Washington Heights.
source: Daily News
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