4 papers
Stochastic Approximation in Banach Spaces Without Geometric Constraints
Rajeeva Laxman Karandikar, B V Rao
The thrust of this article is to show that on all Banach spaces, stochastic approximation holds when the noise sequence is an i.i.d. sequence with mean 0, without imposing any cond…
Revisiting Stochastic Approximation and Stochastic Gradient Descent
Rajeeva Laxman Karandikar, Bhamidi Visweswara Rao, Mathukumalli Vidyasagar
In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is…
Stochastic approximation in infinite dimensions
Rajeeva Laxman Karandikar, Bhamidi V Rao
Stochastic Approximation (SA) was introduced in the early 1950's and has been an active area of research for several decades. While the initial focus was on statistical questions,…
On the Second Fundamental Theorem of Asset Pricing
Rajeeva L Karandikar, B V Rao
Let be sigma-martingales on . We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation…