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UID:3@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20230705T110000
DTEND;TZID=Asia/Kolkata:20230705T120000
DTSTAMP:20231007T192549Z
URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-hybrid-cds-05-july-2
 023%e2%80%b3constrained-stochastic-differential-equations-on-smooth-manifo
 lds/
SUMMARY:Ph.D: Thesis Defense: HYBRID: CDS: ″Constrained Stochastic Differ
 ential Equations on Smooth Manifolds.”
DESCRIPTION:\n\n\n\nSpeaker                 : Mr. Sumit Suthar\n\
 n\nS.R. Number         : 06-18-01-10-12-17-1-14862\n\n\n\n\nTitle  
                      : “Constrained Stochastic Differential E
 quations on Smooth Manifolds.“\n\nResearch Supervisor: Prof. Soumyendu R
 aha\n\n\n\n\n\nDate &amp\; Time         : July 05\, 2023 (Wednesday)\
 , 11:00 AM\n\n\n\n\nVenue                     : The Thesis D
 éfense will be held on HYBRID Mode  # 102 CDS Seminar Hall /MICROSO
 FT TEAMS\n\nPlease click on the following link to join the Thesis Defens
 e:\n\nMS Teams link\n\nhttps://teams.microsoft.com/l/meetup-join/19%3ameet
 ing_YjhkNjhjMzktMjQ2OC00YzYwLTkxZWQtNDJiMWViZDUzYTc0%40thread.v2/0?context
 =%7b%22Tid%22%3a%226f15cd97-f6a7-41e3-b2c5-ad4193976476%22%2c%22Oid%22%3a%
 22f67fa1e8-f789-4048-bb53-c2880088cc5d%22%7d\n\n\n\n______________________
 ____________________________________________________________________\nAbst
 ract\n\n\n\n\n\n\n\n\n\n\n\nDynamical systems with uncertain fluctuations 
 are usually modelled using Stochastic Differential Equations (SDEs). Due 
 to operation and performance related conditions\, these equations may als
 o need to satisfy the constraint equations. Often the constraint equations
  are “algebraic”. Such constraint equations along with the given SDE 
 form a system of Stochastic Differential-Algebraic Equations (SDAEs).\nT
 he main objective of this thesis is to consider these equations on smooth
  manifolds. However\, we first consider SDAEs on Euclidean spaces to unde
 rstand these equations locally. A sufficient condition for the existence 
 and uniqueness of the solution is obtained for SDAEs on Euclidean spaces.
  We also give necessary condition for the existence of the solution. Base
 d on the necessary condition\, there exists a class of SDAEs for which th
 ere is no solution. Since all SDAEs are not solvable\, we present methods
  and algorithms to find approximate solution of the given SDAE.  \nIn o
 rder to extend this work to smooth manifolds\, we consider second order s
 tochastic differential geometry to construct Schwartz morphism to represe
 nt SDEs with drift that are driven by p-dimensional Wiener process. We sh
 ow that it is possible to construct such Schwartz morphisms using what we
  call as diffusion generators. We demonstrate that diffusion generator ca
 n be constructed using flow of second order differential equations\, in p
 articular using regular Lagrangians. The results obtained for SDAEs on Eu
 clidean spaces are extended to SDAEs on smooth manifolds using the framew
 ork of diffusion generators. We show that the results obtained for SDAEs 
 on Euclidean spaces translate to the manifold setting with minimal modifi
 cations. We have derived Ito-Wentzell’s formula on manifolds in the fra
 mework of diffusion generators to obtain approximate bounded solution wit
 h unit probability. Another type of approximate solution is bounded soluti
 on such that the probability of explosion is bounded by α &lt\; 1. We pr
 esent algorithms to compute approximate solutions of both type. This has 
 been demonstrated with an example of SDAE on a sphere.\n=================
 ==============================================================\n\n\n\n\nAL
 L ARE WELCOME\n\n\n\n\n\n
CATEGORIES:Thesis Defense
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