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Stochastic Integrals and Differentials
The Solutions of Stochastic Differential Equations
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an(t analogous Applying arbitrary arguments Assume assumptions boundary condition bounded called coefficients coincides Consequently consider constant converges Corollary corresponding defined definition denote density depend derivatives determine diffusion distribution dw(s dw(t easy equal establish existence and uniqueness exists expectation expression fact finite follows formula function Hence holds independent inequality initial condition integral interval introduce Lemma limit linear Lipschitz condition Markov process means measure moments Moreover o-algebra obtain operator ostST partial Proof properties proved random random field random variables relation Remark right side satisfies second order sense sequence solution space stability stochastic differential equation stochastic equation stochastic integral substitution sufficient Taking Theorem transition probability twice continuously differentiable uniformly v(dt vector Wiener process write zero дх