Math 236, Stochastic Dierential Equations Problem set 3
February 5, 2009
These problems are due on Friday February 13. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Let Xt be
Math 236, Stochastic Dierential Equations Problem set 4
February 17, 2009
These problems are due on Tuesday February 24. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Let X (
Math 236, Stochastic Dierential Equations Solutions to problem set 3
February 17, 2009
Problem 1 Let Xt be the one-dimensional diusion process satisfying the Ito SDE dXt = b(Xt )dt + (Xt )dBt , X0 = x where b(x) and (x) satisfy the Ito conditions (linear
Math 236, Stochastic Dierential Equations Final problem set 6
March 12, 2009
These problems are due on Friday March 20. Please put them in my mailbox outside the mathematics department, slip them under the door of my oce or give them to me in class. Probl
Math 236, Stochastic Dierential Equations Solutions for problem set 2
February 5, 2009
Problem 1 Let 0 = t0 < t1 < t2 < < tN = T be a partition of the interval [0, T ] and let Bt , t 0, be the standard Brownian motion process. Show that
N 1
(Btk+1 Btk )2
Math 236, Stochastic Dierential Equations Problem set 5
March 7, 2009
These problems are due on Friday March 13. Please put them in my mailbox outside the mathematics department, slip them under the door of my oce or give them to me in class. Problem 1 Co
Math 236, Stochastic Dierential Equations Problem set 1
January 13, 2009
These problems are due on Tuesday January 20. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 The stati
AN INTRODUCTION TO STOCHASTIC DIFFERENTIAL EQUATIONS VERSION 1.2
Lawrence C. Evans Department of Mathematics UC Berkeley
Chapter 1: Introduction Chapter 2: A crash course in basic probability theory Chapter 3: Brownian motion and white noise Chapter 4: St
Homework 4 Solutions
March 11, 2009
Problem 1. Using Itos formula on XX T d(XX T ) = (dX )X T + X dX T + dX (dX )T = (AX dt + dB )X T + X (X T AT dt + dB T T ) + dB dB T T = AXX T dt + dBX T + XX T AT dt + dB T T + T dt where weve used dB dB T = I dt1 . I
Math 236, Stochastic Dierential Equations Problem set 2
January 22, 2009
These problems are due on Friday January 30. 5pm. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Let 0
Homework 1 Solutions
January 24, 2009
Problem 1 First we check that X (t) is stationary. Let (a1 , . . . , an ) be any n-tuple with ai = 1. We need to verify that P (X (t1 ) = a1 , X (t2 ) = a2 , . . . , X (tn ) = an ) = P (X (t1 + h) = a1 , X (t2 + h) =