Abstract
For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures\(\mu _{(\xi ^{(n)} ,w)} \),n=1, ... , associated with the solutions, to the limiting measure\( \mu _{(\xi ^{(0)} ,w)} \). The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well.
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