Pith Number

pith:7UHKYAZB

pith:2020:7UHKYAZBQXP2KVA6RUQ4MVFMTB

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Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals Based on Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs

Dmitriy F. Kuznetsov

Generalized multiple Fourier series enable strong approximation of iterated Ito stochastic integrals for arbitrary multiplicity.

arxiv:2003.14184 v76 · 2020-03-28 · math.PR

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\pithnumber{7UHKYAZBQXP2KVA6RUQ4MVFMTB}

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Claims

C1strongest claim

For the first time we successfully use the generalized multiple Fourier series converging in the sense of norm in L_2([t, T]^k) for the expansion and strong approximation of Ito ISIs of multiplicity k, k in N.

C2weakest assumption

The generalized multiple Fourier series of the integrand converges in L2 norm to the iterated integral itself for arbitrary multiplicity k, without additional restrictions on the weight functions beyond those stated for the Stratonovich case (Chapter 1).

C3one line summary

Develops strong mean-square approximations for iterated stochastic integrals of multiplicity k using generalized multiple Fourier series expansions, with explicit error formulas and applications to numerical solution of Ito SDEs and semilinear SPDEs.

Cited by

2 papers in Pith

Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals Based on Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs

New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process

Receipt and verification

First computed	2026-06-04T01:08:23.796672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd0eac032185dfa5541e8d21c654ac984fe25655c9dbc5b6863d3086f9e35408

Aliases

arxiv: 2003.14184 · arxiv_version: 2003.14184v76 · doi: 10.48550/arxiv.2003.14184 · pith_short_12: 7UHKYAZBQXP2 · pith_short_16: 7UHKYAZBQXP2KVA6 · pith_short_8: 7UHKYAZB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7UHKYAZBQXP2KVA6RUQ4MVFMTB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fd0eac032185dfa5541e8d21c654ac984fe25655c9dbc5b6863d3086f9e35408

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02079e3fe1f1ade3966c9eb1d1ebf106020fa3ed911ba62dd024cd2bcc6dc66c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-03-28T03:22:52Z",
    "title_canon_sha256": "7ca621b560596daf39fcb9aa62efdebde08d9336f8dcb7ced39b5f163237d51b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2003.14184",
    "kind": "arxiv",
    "version": 76
  }
}