the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Let X1 X2 be a sequence of pairwise negatively dependent random variables with distributions F1 F2 on − , and let S n be the maximum of its first n partial sums S1 Sn. This article studies the asymptotic tail probabilities of Sn and S n . Under suitable regularity conditions on the distributions F1 Fn, we prove that both P Sn > x and P S n > x are asymptotic to ∑n i=1 1− Fi x as x → , indicatin...

R , U ) and (Uk ,Uk) ) , k = 1,2 , . . . , N , are measurable spaces and J k , k = 1,2 , . . . , N , are subfields of the product field 13@(@, U i ) . Consider an N-tuple of functions y := ( y l , y2 , . . . , y N ) for which yk , k = 1,2 , . . . , N , is J k / U k measurable. If for each w E 0 there exists a unique u := ( u l , u2 , . . . , u N ) E nLl U i satisfying the equations u k = yk(w, ...

s of PhD Theses at Irish Universities 2010 Supersymmetric Quantum Stochastic Analysis